Is there a way to find the transfer function from only your input and the steady state response?

I know that a transfer function has the general form of $$G(S) = Y(S)/U(S)$$ where $Y(S)$ is the output and $U(S)$ is the input.

However, if given the output $u(t)$ and the steady state response $y_{ss}(t)$, is is still possible to obtain your transfer function?

Is there a way to find the transfer function from only your input and the steady state response?

Clearly, no. Steady state response means assentially the 0 frequency response. Obviously systems can have the same 0 frequency (DC) response but various responses to other frequencies.

For example, consider a simple R-C low pass filter. The DC response is simply 1 (output = input), but that is not true of higher frequencies. Different values of R and C will have different frequency profiles, but all have the same response to DC.

Or consider a simple R-C high pass filter. The DC response is 0, but obviously that is not true of other frequencies.